$($b$)$ Given the following logic circuit:

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i$.$ Find a Boolean expression for the output $Q$ for this logic circuit.

ii$.$ Use the laws of Boolean algebra to simplify the output of the above circuit.

$($c$)$ Use the duality principle to find out the dual of the following equation:

$a\frac{+}{b}ar(((\frac{?}{\text{b}\text{a}\text{r}}(b))+a).b)harr1$

$($d$)$ For the following Boolean expression, give:

$F(A,B,C)\frac{?}{b}=ar(A)*B*C+A\frac{*}{b}ar(B)*C+A*B*C$

i$.$ The truth table.

ii$.$ The Karnaugh map.

iii. The minimal sum of products expression.

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